2024年-R語言與數(shù)據(jù)描性分析

1第二節(jié)R與數(shù)據(jù)描述性分析描述統(tǒng)計(jì)分析推斷統(tǒng)計(jì)分析繪制統(tǒng)計(jì)圖型編制統(tǒng)計(jì)表格計(jì)算描述統(tǒng)計(jì)量參數(shù)估計(jì)假設(shè)檢驗(yàn)數(shù)據(jù)建模數(shù)據(jù)挖掘…數(shù)據(jù)的統(tǒng)計(jì)分析張金龍R初步2010-6-322.1用統(tǒng)計(jì)量描述數(shù)據(jù)R基本統(tǒng)計(jì)分析函數(shù)命令解釋max(x)返回向量x中最大元min(x)返回向量x中最小元which.max(x)返回x最大元的下標(biāo)which.min(x)返回x最小元的下標(biāo)mean(x)計(jì)算樣本x的均值median(x)計(jì)算樣本x的中位數(shù)var(x)計(jì)算樣本x的方差sd(x)計(jì)算樣本x的標(biāo)準(zhǔn)差fiveenum(x)計(jì)算樣本x的五數(shù)概括quantile(x,pro=c())計(jì)算樣本x的常用分位數(shù)（默認(rèn)五數(shù)概括）summary(x)計(jì)算樣本x的（五數(shù)概括+均值）張金龍R初步2010-6-33sum(x)(cumsum(x))給出樣本x的總和(積累和）mad(x)計(jì)算中位絕對(duì)離差1.4826median(abs(x-median(x)))range(x)返回向量c(min(x),max(x))或(min(x)-max(x))IQR(x)計(jì)算樣本x的四分位數(shù)極差sort(x)sort(x)按升序排序,選項(xiàng)decreasing=TRUE表降序skewness(x)樣本的偏度系數(shù)（需加載fBasics程序包）kurtosis(x)樣本的峰度系數(shù)（需加載fBasics程序包）basicStats(x)fBasics包中的命令,計(jì)算常用的統(tǒng)計(jì)量Stat.desc(x)Pastecs包中命令，計(jì)算多個(gè)統(tǒng)計(jì)量和均值置信區(qū)間Describe.by(x)psych包,Hmise包中命令，計(jì)算常用的統(tǒng)計(jì)特征量var(x,y)，cov(x,y)計(jì)算樣本x,y的協(xié)方差或協(xié)方差矩陣cor(x,y)計(jì)算樣本x,y的相關(guān)系數(shù)col(row)means(x)矩陣x行(列)均值scale(x,center=T)對(duì)矩陣或數(shù)據(jù)框x中心化，(,+scale=T)標(biāo)準(zhǔn)化aggregate(x,by,fun)對(duì)數(shù)據(jù)框x的指定分組變量按指定函數(shù)統(tǒng)計(jì)分析apply(s,t,lpply)對(duì)矩陣（列表或向量、因子）指定分組變量使用函數(shù)張金龍R初步2010-6-34張金龍R初步2010-6-352.1.1一維數(shù)據(jù)分布的特征數(shù)據(jù)水平(位置)數(shù)據(jù)差異

(分散程度)分布形狀(偏態(tài)和峰態(tài))張金龍R初步2010-6-36（一）水平的度量（數(shù)據(jù)的“位置”）1.均值

mean()消除了觀測(cè)值的隨機(jī)波動(dòng)易受極端值的影響2.

中位數(shù)median()me50%50%排序后處于中間位置上的值。不受極端值影響張金龍R初步2010-6-37其中x(i)是第i個(gè)順序統(tǒng)計(jì)量的樣本值，按升序排列為：x(1)≤x(2)≤…≤x(n)在R中，sore()給出樣本的次序統(tǒng)計(jì)量的觀察值。sore(x):數(shù)據(jù)按升序排列,decreasing=TRUE

為降序。sore(x,na):有缺失值的數(shù)據(jù)，不處理缺失數(shù)據(jù)。sore(x,na.last=T):排序保留缺失數(shù)據(jù)，排在最后。sore(x,na.last=F):排序保留缺失數(shù)據(jù)，排在最前。與sore(x)相關(guān)的函數(shù)：

order()給出排序后的下標(biāo)。

rank()給出樣本的秩統(tǒng)計(jì)量。張金龍R初步2010-6-38set.seed(1);z=sample(1:100,9);z#設(shè)置種子，在1~100中任取9個(gè)數(shù)，比較與sample(1:100,9,rep=T)和去掉set.seed(1)的不同,

[1]273757892086976258sort(z)[1]202737575862868997sort(z,decreasing=TRUE)[1]978986625857372720order(z)

[1]

512398647z[order(z)]

[1]273757892086976258which(z==max(z))#給出最大值下標(biāo),等價(jià)于which.max[1]7which(z==median(z))#給出中位數(shù)下標(biāo)[1]9例2.1

（排序，次序統(tǒng)計(jì)量的樣本值，最大值、中位數(shù)下標(biāo))

張金龍R初步2010-6-393.眾數(shù)(mode)：一組數(shù)據(jù)中出現(xiàn)次數(shù)最多的變量值適合于數(shù)據(jù)量較多時(shí)使用不受極端值的影響一組數(shù)據(jù)可能沒有眾數(shù)或有幾個(gè)眾數(shù)momo在R中，樣本x的眾數(shù)如下計(jì)算：which(table(x)==max(table(x)))例2.1

x<-c(2,2,4,4,4,6,6,6,8)

table(x)#x的頻數(shù)表

max(table(x))#眾數(shù)出現(xiàn)的次數(shù)

which(table(x)==max(table(x)))#

眾數(shù)在table(x)第幾個(gè):4,6.張金龍R初步2010-6-310左偏分布均值

中位數(shù)

眾數(shù)對(duì)稱分布

均值=

中位數(shù)=

眾數(shù)右偏分布眾數(shù)

中位數(shù)均值眾數(shù)、中位數(shù)和平均數(shù)的關(guān)系均值是觀測(cè)值的重心：對(duì)稱分布或接近對(duì)稱分布時(shí)代表性較好中位數(shù)是觀測(cè)值的中心：數(shù)據(jù)分布偏斜程度較大時(shí)代表性接好眾數(shù)是觀測(cè)值的重點(diǎn)：偏斜程度較大且有明顯峰值時(shí)代表性較好張金龍R初步2010-6-3114.

分位數(shù)quantile()p分位數(shù)上四分位數(shù)下四分位數(shù)1stQu3stQu、quantile(x):給出0%，25%，50%，75%，100%分位數(shù)。quantile(x，prob=seq(0,1,0.2),na.rm=TRUE):給出0%，20%，40%，60%，80%，100%分位數(shù)，且可處理缺失值。quantile(x，(0,25,0.75)):給出25%，75%分位數(shù)。張金龍R初步2010-6-3125.最大值

max()

與最小值min()6.五數(shù)概括fiveenum(x)或quantile(x)Min,1stQu,Median,3stQu,Max7.描述統(tǒng)計(jì)量summary()Min.1stQu.MedianMean3rdQu.Max.8.截尾

trimmed

()比如：Trimmed=0.2基于中間60%的數(shù)據(jù)，最高和最低20%的數(shù)值被忽略張金龍R初步2010-6-313占25%數(shù)據(jù)量位置的分位數(shù)50%位置的分位數(shù)占75%數(shù)據(jù)量位置的分位數(shù)最大

觀測(cè)值最小

觀測(cè)值中位數(shù)上四分位數(shù)下四

分位數(shù)(1stQuartile）（3stquartile）有50%的觀測(cè)值小于中位數(shù)有50%的觀測(cè)值位于上下四分位數(shù)之間有50%的觀測(cè)值大于中位數(shù)四分位數(shù)五數(shù)概括按照位置來確定四分位數(shù)meX(n)X(1)張金龍R初步2010-6-314（二）差異的度量（數(shù)據(jù)的“尺度”）1.方差

var()2.標(biāo)準(zhǔn)差sd()3.變異系數(shù)CV=100×sd()/mean()對(duì)數(shù)據(jù)相對(duì)離散程度的測(cè)度消除了數(shù)據(jù)水平高低和計(jì)量單位的影響用于對(duì)不同組別數(shù)據(jù)離散程度的比較張金龍R初步2010-6-3154.樣本矯正平方和CSS=CSS<-sum(x-mean(x))^2),CSS5.樣本未矯正平方和USS=USS<-sum(x^2),USS6.極差rang=max(x)-

min(x)=x(n)-x(1)R<-max(x)-min(x)7.四分位差I(lǐng)QR(x)反映了中間50%數(shù)據(jù)的離散程度不受極端值的影響用于衡量中位數(shù)的代表性離散程度的最簡(jiǎn)單測(cè)度值易受極端值影響未考慮數(shù)據(jù)的分布張金龍R初步2010-6-316異常值：x>上四分位數(shù)+1.5×（上四分位數(shù)-下四分位數(shù)）x<下四分位數(shù)-1.5×（上四分位數(shù)-下四分位數(shù)）極端異常值：x>上四分位數(shù)+3×（上四分位數(shù)-四百分位數(shù)）x<下四分位數(shù)-3×（上四分位數(shù)-四百分位數(shù)）10.異常(極端)值8.標(biāo)準(zhǔn)誤SE.mean:SE.mean<-sd(x)/n^0.5盒型圖中有顯示9.中位數(shù)絕對(duì)離差函數(shù)mad():mad(x)=1.4826*median(abs(x-median(x)))該數(shù)約等于1/qnorm(3/4),保證正態(tài)或大樣本下對(duì)標(biāo)準(zhǔn)差估計(jì)的一致性張金龍R初步2010-6-317（三）分布形態(tài)的度量左偏分布偏態(tài)右偏分布扁平分布尖峰分布與標(biāo)準(zhǔn)正態(tài)分布比較！峰態(tài)Sk<0Sk>0K<0K>0張金龍R初步2010-6-3181.偏度系數(shù)skewness()2.峰度系數(shù)kurtosis()需加載包：fBasics,Pastecs,psych等對(duì)分布曲線尖削程度的測(cè)度K<0,平緩K>0,尖峭對(duì)分布偏斜方向和程度的測(cè)度Sk<0,左偏Sk>0,右偏張金龍R初步2010-6-3192.1.2多維數(shù)據(jù)的特征分析對(duì)多維數(shù)據(jù)，可認(rèn)為來自多元總體，除了分析各個(gè)分量的取值特征，這些是進(jìn)行比較或區(qū)分的根據(jù)，更重要的分析各分量之間的相關(guān)關(guān)系，對(duì)多元數(shù)據(jù)的相關(guān)分析，是多元統(tǒng)計(jì)分析的基礎(chǔ)。假設(shè)n元數(shù)據(jù)集張金龍R初步2010-6-320201.樣本均值mane()矩陣形式其中張金龍R初步2010-6-321212.樣本協(xié)方差矩陣cov()sjk=skj

，cov(X)是對(duì)稱矩陣。張金龍R初步2010-6-322223.樣本相關(guān)系數(shù)矩陣cor()其中張金龍R初步2010-6-323234.數(shù)據(jù)的中心化和標(biāo)準(zhǔn)化處理中心化：標(biāo)準(zhǔn)化：其中scale(x,center=T)scale(x,center=T，scale=T)此時(shí)張金龍R初步2010-6-324例2.3

a<-read.table("Billianaires.TXT",sep=",",header=T,na.string="-")#讀取文本“Billianaires.TXT”，?？怂垢缓琅判邪駭?shù)據(jù).(1)對(duì)單組數(shù)據(jù)a[3]=Net.Worth的描述統(tǒng)計(jì)afivenum(a$Net.Worth)[1]1.01.42.13.669.0quantile(a$Net.Worth,prob=c(0.25,0.5,0.75))25%50%75%1.42.13.6

quantile(a$Net.Worth)0%25%50%75%100%1.01.42.13.669.0

summary(a$Net.Worth)

Min.1stQu.MedianMean3rdQu.Max.1.0001.4002.1003.7343.60069.000which(table(a[3])==max(table(a[3])))1.13

眾數(shù)是1.1張金龍R初步2010-6-325

library(fBasics)basicStats(a$Net.Worth)X..a.Net.Worthnobs1223.000000NAs0.000000Minimum1.000000Maximum69.0000001.Quartile1.4000003.Quartile3.600000Mean3.733688Median2.100000Sum4566.300000SEMean0.146241LCLMean3.446777UCLMean4.020598Variance26.155456Stdev5.114240Skewness5.386001Kurtosis44.748740library(pastecs)stat.desc(a[3])

Net.Worthnbr.val1223.0000000nbr.null0.0000000nbr.na0.0000000min1.0000000max69.0000000range68.0000000sum4566.3000000median2.1000000mean3.7336877SE.mean0.1462406CI.mean.0.950.2869105var26.1554559std.dev5.1142405coef.var1.3697558附注：均值95%置信區(qū)間：（mean

±CI.mean.0.95)

張金龍R初步2010-6-326

RankNameNet.WorthMin.:1.0RobertMiller:2Min.:1.0001stQu.:304.0A.JerroldPerenchio:11stQu.:1.400Median:601.0AbdulAzizAlGhurair&family:1Median:2.100Mean:596.6AbdullaAlFuttaim:1Mean:3.7343rdQu.:913.0AbdullahAlRajhi:13rdQu.:3.600Max.:1153.0AbigailJohnson:1Max.:69.000(Other):1216AgeSourceCountry.of.CitizenshipMin.:0.00realestate:70UnitedStates:4211stQu.:52.00diversified:58Russia:96Median:62.00investments:50China:95Mean:62.39retail:46Germany:553rdQu.:72.00hedgefunds:29India:48Max.:101.00banking:28HongKong:38NA's:32(Other):942(Other):4701.summary(a)該函數(shù)可同時(shí)對(duì)多組數(shù)據(jù)進(jìn)行分別概述，注意結(jié)果合理性(2)對(duì)多組數(shù)據(jù)的描述統(tǒng)計(jì)張金龍R初步2010-6-327summary(a[,c(3,4)])

Net.WorthAgeMin.:1.000Min.:0.001stQu.:1.4001stQu.:52.00Median:2.100Median:62.00Mean:3.734Mean:62.393rdQu.:3.6003rdQu.:72.00Max.:69.000Max.:101.00NA's:32對(duì)于分類變量Source和Country.of.Citizenship可考慮：按頻數(shù)排序，并找到眾數(shù)，中位數(shù)等sort(table(a[,6]))which(table(a[,6])==median(table(a[,6])))which(table(a[,6])==max(table(a[,6])))張金龍R初步2010-6-328

788MalaysiaSwitzerlandMexico9911SwedenIsraelFrance111315ItalySpainIndonesia161617AustraliaSouthKoreaJapan182024TaiwanCanadaTurkey242634UnitedKingdomBrazilHongKong363738IndiaGermanyChina485595RussiaUnitedStates96421

>which(table(a[,6])==median(table(a[,6])))#頻數(shù)中位數(shù)對(duì)應(yīng)地區(qū)或國(guó)家

AustriaLebanonNetherlandsPhilippines3293439>which(table(a[,6])==max(table(a[,6])))#頻數(shù)最大值對(duì)應(yīng)地區(qū)或國(guó)家UnitedStates58張金龍R初步2010-6-329

2.library(psych)describe(a)

varsnmeansdmediantrimmedmadminRank11223596.58342.25601.0597.73452.191Name*21223611.76352.88612.0611.83453.681Net.Worth312233.735.112.12.601.261Age4119162.3913.6162.062.244.830Source*51223266.03138.99262.0268.16174.951Country.of.Citizenship*6122338.5419.8843.040.1822.241maxrangeskewkurtosisseRank11531152-0.01-1.219.79Name*122212210.00-1.2010.09Net.Worth69685.3944.750.15Age101101-0.100.300.39Source*519518-0.10-1.123.97Country.of.Citizenship*5958-0.44-1.410.57該函數(shù)可對(duì)多組數(shù)據(jù)的描述統(tǒng)計(jì)量同時(shí)進(jìn)行概述，注意結(jié)果合理性,*號(hào)的不適合用張金龍R初步2010-6-330library(psych)describe(a[,3:4])

varsnmeansdmediantrimmedmadminmaxNet.Worth112233.735.112.12.601.26169Age2119162.3913.6162.062.2414.830`rangeskewkurtosisseNet.Worth685.3944.750.15Age101-0.100.300.39

3.aggregat(x,by,fun)aggregate(a[,3],list(a[,6]),mean)#計(jì)算不同國(guó)家富豪平均財(cái)富X為數(shù)據(jù)框by指定分類變量Fun指出統(tǒng)計(jì)函數(shù)，比如mean另有apply,tapply,sapply,lapply等函數(shù)也用來處理多組數(shù)據(jù)的描述統(tǒng)計(jì)4.cov(),cor()#多元數(shù)據(jù)相關(guān)性分析張金龍R初步2010-6-331二、頻數(shù)（率）表描述數(shù)據(jù)適合數(shù)據(jù)類型：1.離散值變量.2.定性變量（分類數(shù)據(jù)）.3.連續(xù)值變量離散化（分組）.命令解釋table()樣本的頻數(shù)表，多類別因子的k維頻數(shù)表（列聯(lián)表）xtabs(formula,data)根據(jù)公式或數(shù)據(jù)框或矩陣創(chuàng)建一個(gè)列聯(lián)表prop.table()（*100）頻數(shù)表轉(zhuǎn)化為頻率（百分比）margin.table(table,)邊際頻數(shù)表addmargin(table,)邊際累加頻數(shù)表prop.table(table,)邊際頻率表ftable(table）緊湊多維頻數(shù)表R中常用頻數(shù)，頻率表即列聯(lián)表函數(shù)張金龍R初步2010-6-332library(MASS)quineattach(quine)table(Age)table(Sex,Age);tab=xtabs(~Sex+Age,quine);unclass(tab)tapply(Days,Age,mean)tapply(Days,list(Sex,Age),mean)張金龍R初步2010-6-3331.離散值數(shù)據(jù)>table(a[,4])#富豪年齡頻數(shù)表

0272829303132333435363738394041424344

3211211123215813951421

45464748495051525354555657585960616263

21242430272926292626283132373041293624

64656667686970717273747576777879808182

28253630362832272018272418211417121915

83848586878889909192939496101

1415131561272541311例2.4b<-read.table("某地區(qū)畢業(yè)生調(diào)查.txt“,header=T);b>table(b[,4])#花費(fèi)時(shí)間頻數(shù)表

0

1

2

3

4

5

6

7

8

9

10

1215

363

24416763

22

71

3

3

1

2

1張金龍R初步2010-6-3342.定性或分類數(shù)據(jù)

table(b[,6],b[,7])#“學(xué)校層次”與“是否找到工作”頻數(shù)表12

3

09013242

199380212

prop.table(table(b[,6],b[,7]))*100#相應(yīng)頻率表

123

09.42408413.8219904.397906

110.36649239.79057622.198953prop.table(table(b[,1],b[,6]))#“性別”與“是否找到工作頻率

0110.12041880.3026178

20.15602090.4209424張金龍R初步2010-6-3353.連續(xù)值數(shù)據(jù)分組

s<-factor(cut(b[,3],breaks=0+20*(0:7)))table(s)s(0,20](20,40](40,60](60,80](80,100]4853659157b$cl<-s;b;table(b[,5],b[,11])張金龍R初步2010-6-336R中數(shù)據(jù)分布相關(guān)的基本作圖函數(shù)命令解釋pie(x)餅圖boxplot(x)箱形圖polygon(x,y)繪多邊形hist(x,breaks=“”,freq=T,)頻率直方圖(分組組距,頻率(數(shù)),標(biāo)題,坐標(biāo).填充色等)barplot(x)x的條形圖density(x,…)直方圖上核密度估計(jì)曲線ecdf(x)經(jīng)驗(yàn)分布函數(shù)stem(x)莖葉圖pplot(x,y,…)散點(diǎn)圖par(mfrow=c(,)根據(jù)向量c(,)按行分割圖形par(mfcol=c(,)根據(jù)向量c(,)按列分割圖形stars(x)星圖2.2用圖形描述數(shù)據(jù)分布張金龍R初步2010-6-337利用圖表表示數(shù)據(jù)時(shí)，首先要確定數(shù)據(jù)所屬類型是定性數(shù)據(jù)還是定量數(shù)據(jù)定性數(shù)據(jù)常用的圖形表示：條形圖餅圖定量數(shù)據(jù)常用的圖形表示：直方圖莖葉圖箱線圖散點(diǎn)圖核密度估計(jì)圖雷達(dá)、星形圖臉譜圖小提琴圖…張金龍R初步2010-6-3382.2.1.直方圖hist()hist(x,breaks="Sturges",freq=T,probability=!freq,…)break規(guī)定了直方圖的組距(必須覆蓋數(shù)據(jù)的范圍)；freq是邏輯變量，TRUE是頻率直方圖，F(xiàn)ALSE是密度直方圖；probability和freq相反，par(mfrow=c(1,3))hist(a$Net.Worth)hist(a$Net.Worth,freq=F，col=“red”)hist(a$Net.Worth,freq=F,xlab="Net.Worth")張金龍R初步2010-6-3392.2.2.核密度估計(jì)density()用density()函數(shù)可以繪制與直方圖配套的核密度估計(jì)。density的一般用法為：

density(x,bw="nrd0",adjust=1,kernel=c("gaussian","…"),window=kernel,width…)bw是帶寬，默認(rèn)值R畫出光滑圖形；kernel是核函數(shù)；adjust表示實(shí)際帶寬是adjust*bw。張金龍R初步2010-6-340w<-c(75,64,47.4,66.9,62.2,62.2,58.7,63.5,66.6,64,57,69,56.9,50,72)hist(w,freq=F);lines(density(w),col="blue")x<-44:76;lines(x,dnorm(x,mean(w),sd(x)),col="red")張金龍R初步2010-6-341若要在R中畫出經(jīng)驗(yàn)分布函數(shù)，則用plot函數(shù)：

plot(ecdf(x),ylab="Fn(x)",verticals=FALSE,col.01line="gray70")verticals是邏輯變量，TRUE時(shí)表示畫豎線，否則不畫豎線；col.01line是0-1線的顏色。

plot(ecdf(w),verticals=T)；

x<-44:78;lines(x,pnorm(x,mean(w),sd(w)))2.2.3.經(jīng)驗(yàn)分布函數(shù)ecdf()張金龍R初步2010-6-3422.2.4.盒型圖boxplot()箱線圖boxplot()直觀地展現(xiàn)數(shù)據(jù)分布的主要特征，五數(shù)概括的圖形表述。boxplot()有三種基本的用法：

>boxplot(x,…)>boxplot(x,…,range=1.5,width,varwidth,notch=FALSE,outline=TRUE,…,horizontal=FALSE,add=FALSE,at=NULL)>boxplot(formula,data,…,subset,na.action=NULL);x是數(shù)據(jù)構(gòu)成的數(shù)值型向量；range控制了“觸須”的范圍(默認(rèn)值1.5)；notch=TRUE時(shí)，箱線圖帶有切口；outline是邏輯變量，TRUE時(shí)標(biāo)出異常點(diǎn)；horizontal是邏輯變量，TRUE表示把箱線圖繪制成水平狀；

add是邏輯變量，TRUE時(shí)表示在原圖上畫圖，否則替換一張圖。fomular是公式；data給出了公式作用的對(duì)象；subset是可選參數(shù)，給定要繪制的數(shù)據(jù)子集